At the main railway station in Leeds, as the Government's consultation on its new high-speed rail plan drew to a close, twenty police officers held back a 2,000-strong crowd.

They weren't racing to register their support for trains moving at 250mph. They just wanted trains moving at any speed at all.

At the height of Thursday's rush hour, thanks to "power supply problems," the entire rail service out of Yorkshire's biggest city had ground to a halt. It didn't get back to normal until the next day.

On Friday morning, I talked to commuters on the lines into Leeds. In their Yorkshire Posts, the Transport Secretary, Philip Hammond, promised their county would be "among the big winners" from high-speed rail.

Their stations were dotted with posters selling the dream. But they didn't want high-speed trains either. They just wanted trains, of any speed, that they could get on.

"There's not enough carriages," said Jane Robinson, who travels from Headingley. "It is sometimes so crowded that you literally cannot even squeeze in."

On Friday, things were all right. But every single morning outside the holiday season, across West Yorkshire, dozens of commuters are left behind on the platform by trains simply too full to take a single extra person.

As the environmental and economic case for Mr Hammond's £17 billion "HS2" supertrain – initially from London to Birmingham, with extensions to Manchester and Leeds - has been increasingly challenged, HS2's supporters have fallen back on another argument: the new capacity it will bring to a crowded rail network.

"The main argument for HS2 is not speed, it's capacity," says David Begg, director of the Yes to High Speed Rail Campaign. "As anyone who uses our railways regularly will tell you, our trains are full and demand for intercity travel is soaring."

Some British trains are, indeed, quite literally full. But the problem with HS2 is that they're not the ones it's going to relieve.

Network Rail says we need HS2 because if trends over the last 15 years continue, the existing line between Euston and Birmingham, the West Coast Main Line, will reach capacity by 2024.

High-speed opponents challenge the maths, and cite various reasons – home-working, videoconferencing, economic weakness – why the trends of the past may not continue.

But even if the forecast is right, it seems odd to spend so much on a potential capacity problem in thirteen years' time when we have an actual capacity crisis on many other parts of the network right now.

At least one other main line – the East Coast, London to Yorkshire and the North East – is full already, according to Network Rail.

There is already an alternative route to Birmingham, from Marylebone, which has just had a £250 million upgrade. And the real problems are not on the main lines, but on the commuter services which the vast majority of passengers use.

Over the last decade, local routes in West Yorkshire have seen passengers rise by 50 per cent. But the number of seats has risen by only 11 per cent.

Most services are still run by 25-year-old, two and three-car diesel railbuses more suited to a country branch line.

Yorkshire's commuter trains are now the country's most crowded, outside London.

Under the second phase of HS2, in about 20 years' time, Leeds gets 20 minutes off its journey time to the capital. But the London service is already fast, frequent, electric – and less crowded than the commuter routes.

Leeds' burning transport need is for better local services, not further improvement to one of the few decent trains it already has.

As a study by the London School of Economics found, improving transport within conurbations has far greater economic and social benefits than improving transport between them.

On the Headingley and Harrogate line, one of the busiest, they can't run more trains because they still have semaphore signals, unchanged since the nineteenth century.

Most stations don't have ticket offices, or even machines – and the trains are too crowded for the guard to walk through – so when you get to Leeds, you have to queue at the excess fares counter.

"Sometimes you spend longer queuing for a ticket at the other end than you actually spend on the journey," says Andy Lilley, another Harrogate line commuter. "I think HS2's a good idea, but I'd rather have more carriages and a ticket machine."

Leeds is Britain's – possibly Western Europe's - largest city without light rail or a metro. Its public transport consists almost entirely of declining, privatised buses. A light rail scheme was cancelled in 2004, after £40 million had already been spent. Funding for a new trolleybus is on hold.

Ministers insist that local services can be improved too; it's not an "either-or." But in practice, in an austerity era, it seems to be precisely that.

True, West Yorkshire is getting 20 new carriages (it was originally promised 182.) There is talk of new platforms at Leeds' congested station, and extra tracks across the Pennines to Manchester.

But these schemes have not been funded. And while the Government has, as we reveal today, already spent £200 million on HS2, there aren't even proposals for most of the commuter network.

Though supporting high-speed rail, PTEG, the body representing public transport authorities in England's provincial cities, says: "If funding for high-speed rail comes from within existing rail funding sources then it will have a major negative impact on other rail investment, particularly for the North and Midlands, which already suffer from under-investment."

Leeds City Region warns: "Typically 70-80% of all journeys are within city regions. The link between projects such as high-speed rail and local transport is not yet well-made."

Yet even if we accept that the country's most crowded railway is the West Coast Main Line, high-speed rail may not be the best answer to its problems.

In the West Midlands, HS2 will not serve Birmingham New Street, the region's main transport hub. Most people making onward local journeys will have to change stations in central Brum, using the oldest technology of all – a 10-minute walk.

HS2's relative isolation from the rest of the network means many users will stick with the existing service, which does go to New Street, cutting the high-speed train's potential for reducing crowding.

In the first phase of HS2, trains for Manchester and Liverpool, meanwhile, will join the existing line just north of Birmingham, a point where it is already congested. This will displace many existing services, meaning that some places will actually have their train service reduced and even Manchester, which has seen the biggest passenger growth on the whole West Coast route, will get little or no extra capacity.

The Taxpayers' Alliance calculates that – allowing for the imminent arrival of longer trains on the existing line – there could even be a cut, post-HS2, in the number of seats between London and Manchester.

"There is a troubling disconnect between the frequency of services promised and what can credibly be delivered," says Jonathan Tyler, a timetabling expert who has worked in the rail industry for fifty years.

On its other crowded main lines, the East Coast and Great Western, Network Rail is increasing capacity with longer trains and track remodelling to remove pinch-points. On the West Coast, it says, it has exhausted these options already – though regular travellers often wonder why Virgin's Pendolino trains have four first-class carriages, against only five standard-class ones.

Mr Tyler, however, says that there is a whole package of enhancements that could still be done – and that package, known as "RP2" in the rail industry, has not been properly considered as an alternative to a new line. And indeed, a report by the consultants Oxera, commissioned by the Transport Select Committee, found "potential inconsistencies" in the official comparison of the two schemes, with RP2's wider economic benefits omitted from the evaluation, while HS2's were included.

When the economic benefits were included, Oxera found, the benefit-cost ratio of RP2 was "little different" from that for a full-on new line. So for all the sound and fury about HS2, it turns out that we may not even need it.